Archive for October, 2016

Last time we saw how compound pulleys within a dynamic lifting scenario result in increasedmechanical advantage to the lifter, mechanical advantage being an engineering phenomenon that makes lifting weights easier. Today we’ll see how the mechanical advantageincreases when more fixed and movable pulleys are added to the compound pulley arrangement we’ve been working with.

More Pulleys Increase Mechanical Advantage

The image shows a more complex compound pulley than the one we previously worked with. To determine the mechanical advantage of this pulley, we need to determine the force, F5, Mr. Toga exerts to hold up the urn.

The urn is directly supported by four equally spaced rope sections with tension forces F1, F2, F3, and F4. The weight of the urn, W, is distributed equally along the rope, and each section bears one quarter of the load. Mathematically this is represented by,

F1 = F2 = F3 = F4 = W ÷4

If the urn’s weight wasn’t distributed equally, the bar directly above it would tilt. This tilting would continue until equilibrium was eventually established, at which point all rope sections would equally support the urn’s weight.

Because the urn’s weight is equally distributed along a single rope that’s threaded through the entire pulley arrangement, the rope rule, as I call it, applies. The rule posits that if we know the tension in one section of rope, we know the tension in all rope sections, including the one Mr. Toga is holding onto. Therefore,

F1 = F2 = F3 = F4 = F5 = W ÷4

Stated another way, the force, F5 , Mr. Toga must exert to keep the urn suspended is equal to the weight force supported by each section of rope, or one quarter the total weight of the urn, represented by,

F5 = W ÷4

If the urn weighs 40 pounds, Mr. Toga need only exert 10 pounds of bicep force to keep it suspended, and today’s compound pulley provides him with a mechanical advantage, MA, of,

MA = W ÷ F5

MA =W ÷ (W ÷ 4)

MA = 4

It’s clear that adding the two extra pulleys results in a greater benefit to the man doing the lifting, decreasing his former weight bearing load by 50%. If we added even more pulleys, we’d continue to increase his mechanical advantage, and he’d be able to lift far heavier loads with a minimal of effort. Is there any end to this mechanical advantage? No, but there are undesirable tradeoffs. We’ll see that next time.

Last time we introduced the engineering concept of mechanical advantage, MA. Thanks to its presence in our compound pulley arrangement, it made a Grecian man’s job of holding an urn suspended in space twice as easy as compared to when he used a mere simple pulley. Today we’ll see what happens when our static scenario becomes active through dynamic lifting and how it affects his efforts.

Dynamic Lifting is Easier With a Compound Pulley

If you’ll recall from our last blog, Mr. Toga used a compound pulley to assist him in holding an urn stationary in space. To do so, he only needed to exert personal bicep force, F, equivalent to half the urn’s weight force, W, which meant he enjoyed a mechanical advantageof 2. Mathematically that is represented by,

F = W ÷ 2

If the urn weighs 40 pounds, then he only needs to exert 20 Lbs of personal effort to keep it suspended.

But when Mr. Toga uses more bicep power with that same compound pulley, he’s able to dynamically raise its position in space until it eventually meets with the beam that supports it. All the while he’ll be exerting a force greater than W ÷ 2. That relationship is represented by,

F > W ÷ 2

In the case of a 40 Lb urn, the lifting force Mr. Toga must exert to dynamically lift the urn is represented by,

F > 40 Lbs ÷ 2

F > 20 Lbs

where F represents a bicep force of at least 20 pounds. Fortunately for him, his efforts will never have to extend much beyond 20 Lbs of effort to lift the urn to the beam. That’s because gravity’s effect will remain nearly constant as the urn climbs, this being due to gravity’s influence upon objects decreasing by an insignificant amount over short distances above the Earth’s surface. As a matter of fact, at an altitude of 3,280 feet, gravity’s pull decreases by a mere 0.2 %.

The net result is that the compound pulley enables the same mechanical advantagewhether a static or dynamic scenario exists, that is, regardless of whether Mr. Toga is simply holding the urn stationary in space or he’s actively tugging on his end of the rope to lift it higher.

Next time we’ll see how mechanical advantageincreases when we add more fixed and moveable pulleys to our compound pulley arrangement.